Laboratory of Structural Methods of Data Analysis in Predictive
Modeling Moscow Institute of Physics and Technology
Finite Sample Bernstein – von Mises Theorem for Semiparametric Problems
The classical parametric and semiparametric Bernstein – von Mises
(BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain an upper bound on the error of Gaussian approximation of the posterior distribution for the target parameter which is explicit in the dimension of the nuisance and target parameters. This helps to identify the so called critical dimension p_n of the full parameter for which the BvM result is applicable. In the important i.i.d. case, we show that the condition “ p_n^3/n is small” is sufficient for the BvM result to be valid under general assumptions on the model. We also provide an example of a model with the phase transition effect: the statement of the BvM theorem fails when the dimension p_n approaches n^{1/3} . The results are extended to the case of infinite dimensional parameters with the nuisance parameter from a Sobolev class.

Авторы: Panov Maxim , Spokoiny Vladimir

Дата: 29 декабря 2014

Статус: в печати

Журнал: Bayesian analysis

Год: 2015

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Statistical methods

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